An opinion is a subjective belief, based on perspective, emotion, or a persons perception of something. Knowledge is based on fact and something that can be supported by empirical, repeatable evidence.

An opinion is a subjective belief, based on perspective, emotion, or a persons perception of something.

Exactly. And because everything is a matter of perception (there is no such thing as escaping your own perspective), everything is technically subjective.

Knowledge is based on fact and something that can be supported by empirical, repeatable evidence.

Actually, empiricism isn't objectively true. Let me explain why.

Empiricism is based on the Correspondence Theory of Truth. However, the correspondence theory of truth is not fact, it's an assumption which is made for practical purposes. People, however, are under no obligation to accept it, if they choose not to. And if they choose not to, they don't have to accept empiricism at all.

This is most clear when discussing solipsism. What is solipsism? It's simply the realization that you can never provide proof or evidence that your sense are accurate. Because you can never provide evidence that your senses are accurate, you have to assume them if you wish to use them. And that assumption makes things subjective.

That's sort of why everything is technically subjective, even if we consider it universal from our perspective.

How many times does an idea occur? This makes opinions come at infinite possibilities. The saturation of it all is what makes it unequal. However, if you come across a fact, it only has one truth. Everyone will equally know about this fact if they come across it.

That's sort of why everything is technically subjective, even if we consider it universal from our perspective.

Mathematical proofs are not subject to perception or interpretation.

If you accept logic, you'd be correct. Unfortunately, there are people out there who don't even assume logic. Which kinda screws everything over. I haven't actually ever met one, but I have heard they exist. They are nihilists of a certain variety (but not all nihilists reject logic).